In a saucepan, melt butter. Stir in flour until smooth; gradually add broth. Bring to a boil; cook and stir for 2 minutes or until thickened. Remove from the heat. Stir in Monterey Jack cheese, sour cream, chilies, thyme, salt, pepper and remaining cumin.

Spread 1/2 cup of the cheese sauce in a greased 13 x 9 x 2 inch baking dish. Top with 6 tortilla halves, a third of the chicken mixture and a 1/4 of the cheese sauce. Repeat chicken, tortilla and cheese sauce layers twice. Top with remaining tortillas, cheese sauce and Mexican cheese.